Inverse binomial series and values of Arakawa-Kaneko zeta functions - Université Côte d'Azur Access content directly
Journal Articles Journal of Number Theory Year : 2015

Inverse binomial series and values of Arakawa-Kaneko zeta functions

Abstract

In this article, we present a variety of evaluations of series of polylogarithmic nature. More precisely, we express the special values at positive integers of two classes of zeta functions of Arakawa-Kaneko-type by means of certain inverse binomial series involving harmonic sums which appeared fifteen years ago in physics in relation with the Feynman diagrams. In some cases, these series may be explicitly evaluated in terms of zeta values and other related numbers. Incidentally, this connection allows us to deduce new identities for the constant $C= \sum_{n\geq 1} \frac{1}{(2n)^3}(1+\frac13 + \dots + \frac{1}{2n-1})$ considered by S. Ramanujan in his notebooks.
Fichier principal
Vignette du fichier
CentralbinomialSeriesRevised2.pdf (397.8 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-00995770 , version 1 (26-05-2014)
hal-00995770 , version 2 (01-09-2014)
hal-00995770 , version 3 (10-09-2014)
hal-00995770 , version 4 (22-09-2014)
hal-00995770 , version 5 (12-12-2014)

Identifiers

  • HAL Id : hal-00995770 , version 5

Cite

Marc-Antoine Coppo, Bernard Candelpergher. Inverse binomial series and values of Arakawa-Kaneko zeta functions. Journal of Number Theory, 2015, 150, pp.98-119. ⟨hal-00995770v5⟩
286 View
306 Download

Share

Gmail Mastodon Facebook X LinkedIn More